View More View Less
  • 1 University of Wisconsin-Milwaukee Department of Computer Science Milwaukee WI 53201-0784 USA
Restricted access


A set of points in the plane is said to be in general position if no three of them are collinear and no four of them are cocircular. If a point set determines only distinct vectors, it is called parallelogram free. We show that there exist n-element point sets in the plane in general position, and parallelogram free, that determine only O(n2/√log n) distinct distances. This answers a question of Erdős, Hickerson and Pach. We then revisit an old problem of Erdős: given any n points in the plane (or in d dimensions), how many of them can one select so that the distances which are determined are all distinct? — and provide (make explicit) some new bounds in one and two dimensions. Other related distance problems are also discussed.

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Jun 2020 0 0 0
Jul 2020 0 0 0
Aug 2020 3 0 0
Sep 2020 0 0 0
Oct 2020 0 0 0
Nov 2020 1 0 0
Dec 2020 0 0 0